arXiv subjects

Arnab Sen

Publications and source records attributed to Arnab Sen.

At least 55 records · Page 3Linked to original sources

arXiv2021

Quantum scars from zero modes in an Abelian lattice gauge theory on ladders

We consider the spectrum of a $U(1)$ quantum link model where gauge fields are realized as $S=1/2$ spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian $H={\cal O}_{\rm kin}+λ{\cal O}_{\rm pot}$, where ${\cal O}_{\rm pot}$ (${\cal O}_{\rm kin}$) is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at $λ=0$ whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero $λ$ but some special linear combinations that simultaneously diagonalize ${\cal O}_{\rm kin}$ and ${\cal O}_{\rm pot}$ survive as quantum many-body scars, suggesting an ``order-by-disorder'' mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to $56$ spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.

cond-mat.str-el↗

arXiv2021

Mobility edge and multifractality in a periodically driven Aubry-André model

We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-André potential and a hopping amplitude which is varied periodically in time. Our analysis shows the presence of a mobility edge separating single-particle delocalized states from localized and multifractal states in the Floquet spectrum. Such a mobility edge does not have any counterpart in the static Aubry-André model and exists for a range of drive frequencies near the critical frequency at which the transition occurs. The presence of the mobility edge is shown to leave a distinct imprint on fermion transport in the driven chain; it also influences the Shannon entropy and the survival probability of the fermions at long times. In addition, we find the presence of CAT states in the Floquet spectrum with weights centered around a few nearby sites of the chain. This is shown to be tied to the flattening of Floquet bands over a range of quasienergies. We support our numerical studies with a semi-analytic expression for the Floquet Hamiltonian ($H_F$) computed within a Floquet perturbation theory. The eigenspectra of the perturbative $H_F$ so obtained exhibit qualitatively identical properties to the exact eigenstates of $H_F$ obtained numerically. Our results thus constitute an analytic expression of a $H_F$ whose spectrum supports multifractal and CAT states. We suggest experiments which can test our theory.

cond-mat.stat-mech↗

arXiv2021

Coincident angle-resolved state-selective photoelectron spectroscopy of acetylene molecules: a candidate system for time-resolved dynamics

The acetylene-vinylidene system serves as a benchmark for investigations of ultrafast dynamical processes where the coupling of the electronic and nuclear degrees of freedom provides a fertile playground to explore the femto- and sub-femto-second physics with coherent extreme-ultraviolet (EUV) photon sources both on the table-top as well as free-electron lasers. We focus on detailed investigations of this molecular system in the photon energy range $19...40$ eV where EUV pulses can probe the dynamics effectively. We employ photoelectron-photoion coincidence (PEPICO) spectroscopy to uncover hitherto unrevealed aspects of this system. In this work, the role of excited states of the $C_{2}H_{2}^{+}$ cation, the primary photoion, is specifically addressed. From photoelectron energy spectra and angular distributions, the nature of the dissociation and isomerization channels is discerned. Exploiting the $4π$-collection geometry of velocity map imaging spectrometer, we not only probe pathways where the efficiency of photoionization is inherently high but also perform PEPICO spectroscopy on relatively weak channels.

physics.atom-ph↗

arXiv2021

Analytic approaches to periodically driven closed quantum systems: Methods and Applications

We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a Floquet-Magnus resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.

cond-mat.str-el↗

arXiv2020

On $\ell_p$-Gaussian-Grothendieck problem

For $p\geq 1$ and $(g_{ij})_{1\leq i,j\leq n}$ being a matrix of i.i.d. standard Gaussian entries, we study the $n$-limit of the $\ell_p$-Gaussian-Grothendieck problem defined as \begin{align*}\max\Bigl\{\sum_{i,j=1}^n g_{ij}x_ix_j: x\in \mathbb{R}^n,\sum_{i=1}^n |x_i|^p=1\Bigr\}.\end{align*} The case $p=2$ corresponds to the top eigenvalue of the Gaussian Orthogonal Ensemble; when $p=\infty$, the maximum value is essentially the ground state energy of the Sherrington-Kirkpatrick mean-field spin glass model and its limit can be expressed by the famous Parisi formula. In the present work, we focus on the cases $1\leq p<2$ and $2<p<\infty.$ For the former, we compute the limit of the $\ell_p$-Gaussian-Grothendieck problem and investigate the structure of the set of all near optimizers along with stability estimates. In the latter case, we show that this problem admits a Parisi-type variational representation and the corresponding optimizer is weakly delocalized in the sense that its entries vanish uniformly in a polynomial order.

math.PR↗

arXiv2020

Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration

The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars -- eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.

cond-mat.stat-mech↗

arXiv2020

Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach

We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.

cond-mat.str-el↗

arXiv2020

Dynamics of the vacuum state in a periodically driven Rydberg chain

We study the dynamics of the periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0\rangle$) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes ($L\le 26$), that the Floquet Hamiltonian of the system, within a range of drive frequencies which we chart out, hosts a set of quantum scars which have large overlap with the $|0\rangle$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state ($|\mathbb{Z}_2\rangle$); they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0\rangle$ state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing and provide an analytic explanation for this phenomenon. Finally, we demonstrate that for a wide range of drive frequencies, the system reaches a steady state with sub-thermal values of the density-density correlator. The presence of such sub-thermal steady states, which are absent for dynamics starting from the $|\mathbb{Z}_2\rangle$ state, imply a weak violation of the eigenstate thermalization hypothesis in finite sized Rydberg chains distinct from that due to the scar-induced persistent oscillations reported earlier. We conjecture that in the thermodynamic limit such states may exist as pre-thermal steady states that show anomalously slow relaxation. We supplement our numerical results by deriving an analytic expression for the Floquet Hamiltonian using a Floquet perturbation theory in the high amplitude limit which provides an analytic, albeit qualitative, understanding of these phenomena at arbitrary drive frequencies. We discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Restoring coherence via aperiodic drives in a many-body quantum system

We study the unitary dynamics of randomly or quasi-periodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase starting from a $\mathbb{Z}_2$ symmetry-broken state. The randomness is implemented via a telegraph noise protocol in the drive period while the quasi-periodic drive is chosen to correspond to a Thue-Morse sequence. The periodically driven tBH model (with a square pulse protocol characterized by a time period $T$) is known to exhibit transitions from dynamical regimes with long-time coherent oscillations to those with rapid thermalization. Here we show that starting from a regime where the periodic drive leads to rapid thermalization, a random drive, which consists of a random sequence of square pulses with period $T+αdT$, where $α=\pm 1$ is a random number and $dT$ is the amplitude of the noise, restores long-time coherent oscillations for special values of $dT$. A similar phenomenon can be seen for a quasi-periodic drive following a Thue-Morse sequence where such coherent behavior is shown to occur for a larger number of points in the $(T, dT)$ plane due to the additional structure of the drive protocol. We chart out the dynamics of the system in the presence of such aperiodic drives, provide a qualitative analytical understanding of this phenomenon, point out the role of quantum scars behind it, and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2019

Collapse and revival of quantum many-body scars via Floquet engineering

The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite energy density, leads to absence of ergodicity and long-time coherent dynamics in closed quantum systems starting from simple initial states. Such non-ergodic coherent dynamics, where the system does not explore its entire phase space, has been experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and non-ergodic regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the spectrum of the system's Floquet Hamiltonian. The latter regime, in contrast, has scars in its Floquet spectrum which control the long-time coherent dynamics of correlation functions. Our results open a new possibility of drive frequency-induced tuning between ergodic and non-ergodic dynamics in experimentally realizable disorder-free quantum many-body systems.

quant-ph↗

arXiv2019

The dipolar spin glass transition in three dimensions

Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both analytically and numerically because of long-ranged interactions between spins as well as rare region effects. We study a new type of anisotropic dilute dipolar Ising system in three dimensions [Phys. Rev. Lett. {\bf 114}, 247207 (2015)] that arises as an effective description of randomly diluted classical spin ice, a prototypical spin liquid in the disorder-free limit, with a small fraction $x$ of non-magnetic impurities. Metropolis algorithm within a parallel thermal tempering scheme fails to achieve equilibration for this problem already for small system sizes. Motivated by previous work [Phys. Rev. X {\bf 4}, 041016 (2014)] on uniaxial random dipoles, we present an improved cluster Monte Carlo algorithm that is tailor-made for removing the equilibration bottlenecks created by clusters of {\it effectively frozen} spins. By performing large-scale simulations down to $x=1/128$ and using finite size scaling, we show the existence of a finite-temperature spin glass transition and give strong evidence that the universality of the critical point is independent of $x$ when it is small. In this $x \ll 1$ limit, we also provide a first estimate of both the thermal exponent, $ν=1.27(8)$, and the anomalous exponent, $η=0.228(35)$.

cond-mat.dis-nn↗

arXiv2019

Zero-temperature Glauber dynamics on the 3-regular tree and the median process

In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d.~initial spins $σ_x(0)$ from $\{-1,+1\}$ with $\mathbb{P}_p(σ_x(0) = +1)=p$, and they update their spins at the arrival times of i.i.d. Poisson processes to agree with a majority of their neighbors. We study this process on the 3-regular tree $\mathbb{T}_3$, where it is known that the critical threshold $p_c$, below which $\mathbb{P}_p$-a.s. all spins fixate to $-1$, is strictly less than $1/2$. Defining $θ(p)$ to be the $\mathbb{P}_p$-probability that a vertex fixates to $+1$, we show that $θ$ is a continuous function on $[0,1]$, so that, in particular, $θ(p_c)=0$. To do this, we introduce a new continuous-spin process we call the median process, which gives a coupling of all the measures $\mathbb{P}_p$. Along the way, we study the time-infinity agreement clusters of the median process, show that they are a.s. finite, and deduce that all continuous spins flip finitely often. In the second half of the paper, we show a correlation decay statement for the discrete spins under $\mathbb{P}_p$ for a.e. value of $p$. The proof relies on finiteness of a vertex's "trace" in the median process to derive a stability of discrete spins under finite resampling. Last, we use our methods to answer a question of C. Howard (2001) on the emergence of spin chains in $\mathbb{T}_3$ in finite time.

math.PR↗

arXiv2018

Steady states of a quasiperiodically driven integrable system

Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we consider a prototypical integrable spin system, the spin-$1/2$ transverse field Ising model in one dimension, in a pulsed magnetic field. The time dependence of the field is taken to be quasiperiodic by choosing the pulses to be of two types that alternate according to a Fibonacci sequence. We show that a novel steady state emerges after an exponentially long time when local properties (or equivalently, reduced density matrices of subsystems with size much smaller than the full system) are considered. We use the temporal evolution of certain coarse-grained quantities in momentum space to understand this nonequilibrium steady state in more detail and show that unlike the previously known cases, this steady state is neither described by a periodic generalized Gibbs ensemble nor by an infinite temperature ensemble. Finally, we study a toy problem with a single two-level system driven by a Fibonacci sequence; this problem shows how sensitive the nature of the final steady state is to the different parameters.

cond-mat.str-el↗

arXiv2018

Tuning a random field mechanism in a frustrated magnet

We study the influence of spinless impurities on a frustrated magnet featuring a spin-density wave (stripe) phase by means of Monte Carlo simulations. We demonstrate that the interplay between the impurities and an order parameter that breaks a real-space symmetry triggers the emergence of a random-field mechanism which destroys the stripe-ordered phase. Importantly, the strength of the emerging random fields can be tuned by the repulsion between the impurity atoms; they vanish for perfect anticorrelations between neighboring impurities. This provides a novel way of controlling the phase diagram of a many-particle system. In addition, we also investigate the effects of the impurities on the character of the phase transitions between the stripe-ordered, ferromagnetic, and paramagnetic phases.

cond-mat.dis-nn↗

arXiv2018

Ramp and periodic dynamics across non-Ising critical points

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L \le 24$ using exact-diagonalization (ED), of the excitation density $D$, the wavefunction overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ shows Kibble-Zurek scaling. We find, based on numerical analysis with $L \le 24$, that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies $D, Q \to 0$ and $|F| \to 1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

cond-mat.str-el↗

arXiv2017

Periodically driven integrable systems with long-range pair potentials

We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $α$. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after $n \gg 1$ drive cycles for any $α$ and driving frequency $ω$. We introduce a distance measure, $\mathcal{D}_l(n)$, that characterizes the approach of the reduced density matrix of a subsystem of $l$ sites to its final steady state. We chart out the $n$ dependence of ${\mathcal D}_l(n)$ and identify a critical value $α=α_c$ below which they generically decay to zero as $(ω/n)^{1/2}$. For $α> α_c$, in contrast, ${\mathcal D}_l(n) \sim (ω/n)^{3/2}[(ω/n)^{1/2}]$ for $ω\to \infty [0]$ with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing $n$ for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for $ω< ω^{(1)}_c$, where $ω^{(1)}_c$ is the largest critical frequency for the dynamical transition for a given $α$. One such feature is the presence of {\it multiple} light cone-like structures which persists even when $α$ is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with $α\le 2$ differs qualitatively from their short-ranged counterparts with $α> 2$ for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.

cond-mat.str-el↗

arXiv2017

Aperiodically driven integrable systems and their emergent steady states

Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as "geometric generalized Gibbs ensemble", that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.

cond-mat.str-el↗

arXiv2017

Duality between the deconfined quantum-critical point and the bosonic topological transition

Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.

cond-mat.str-el↗